2x(34+5x)=7x-89

Solution for 2x(34+5x)=7x-89 equation:

2x(34+5x)=7x-89

We move all terms to the left:

2x(34+5x)-(7x-89)=0

We add all the numbers together, and all the variables

2x(5x+34)-(7x-89)=0

We multiply parentheses

10x^2+68x-(7x-89)=0

We get rid of parentheses

10x^2+68x-7x+89=0

We add all the numbers together, and all the variables

10x^2+61x+89=0

a = 10; b = 61; c = +89;
Δ = b2-4ac
Δ = 612-4·10·89
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-\sqrt{161}}{2*10}=\frac{-61-\sqrt{161}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+\sqrt{161}}{2*10}=\frac{-61+\sqrt{161}}{20}
$